Aggregating marginal heatmaps.
Our model is trained jointly to predict the intermediate heatmaps as well as the normalized skeletal coordinates. We apply the soft-argmax operator [1]} to extract the normalized coordinates of each joints onto the \(xy\) , \(xz\) , and \(yz\)  planes. We choose the predictions from the \(xy\) -plane for the \(xy\)  coordinate of the final prediction \(\hat{p}_{xyz}\) , as they match naturally with the input image. For \(z\) , we average the \(zy\)  and \(xz\)  predictions. Eq. REF  summarizes these steps as:
\(\begin{split}\hat{H}^i_{xy}, H^i_{xz}, \hat{H}^i_{yz} = \text{Model}(\mathbf {x}) \\\begin{bmatrix}x^i_{xy}, y^i_{xy}\end{bmatrix}= \text{soft-argmax}(\hat{H}^i_{xy}) \\\begin{bmatrix}x^i_{xz}, z^i_{xz}\end{bmatrix}= \text{soft-argmax}(\hat{H}^i_{xz}) \\\begin{bmatrix}y^i_{zy}, z^i_{zy}\end{bmatrix}= \text{soft-argmax}(\hat{H}^i_{zy}) \\\hat{p}^i_{xyz} = \begin{bmatrix}x^i_{xy}, y^i_{xy}, \frac{z^i_{xz} + z^i_{zy}}{2}\end{bmatrix}.\end{split}\) 
